Cross guild? Definitely sounds like a name Mihawk would choose, and not Buggy. Buggy would have gone with something much flashier considering his personality.
How much do people want to bet that Mihawk is playing the ‘man behind the man’ role, leveraging Buggy’s attention whoring and previous role on Roger’s crew to make him the figurehead while Mihawk chills in the background? I can definitely see him in the same role as Katakuri, the one who actually gets shit done while the ‘leader’ is being stupid and/or batshit insane.